Analytical representation of stock and stock-indexes returns: Non-Gaussian random walks with various jump laws

► Random walk process with a specific jump law is proposed for asset returns. ► Random walk distributions are derived from a general conception of stochastic jumps. ► Our model covers Gauss random walks, Levy flights as well as truncated Levy walks. ► The natural generalization of truncated Levy walks is done. ► There is a good agreement of the theory with empirical data for returns of assets.